Theorems · Theorem · general topology
Metric.eball_subset_closedEBall
∀ {α : Type u} [inst : PseudoEMetricSpace α] {x : α} {ε : ENNReal}, Metric.eball x ε ⊆ Metric.closedEBall x ε- Defined in
- Mathlib.Topology.EMetricSpace.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- ENNRealstatement and proof · cited by 9,879
- PseudoEMetricSpacestatement and proof · cited by 1,536
- le_of_ltproof · cited by 1,175
- Metric.eballstatement and proof · cited by 294
- Metric.closedEBallstatement · cited by 107
- Membership.mem.outproof · cited by 38
Cited by5
Results whose statement or proof uses this declaration.
- Metric.closedEBall_mem_nhdsproof · cited by 4
- Metric.ediam_eball_leproof · cited by 2
- EMetric.subset_countable_closure_of_compactproof · cited by 1
- Metric.measure_closedEBall_posproof · cited by 1
- EMetric.ball_subset_closedBallproof · cited by 0